The Nikkei 225 index at the Tokyo Stock Exchange gained 66.62 points to 17,424.13 by the break, while the Topix index of all first-section issues climbed 0.60 percent, or 8.35 points, to 1,408.53.
Tokyo markets were closed Monday for a national holiday.
“Despite the bullish market, solid earnings reports have kept price-to-earnings levels reasonable, so the market is not expensive from a valuation perspective,” said Takashi Matsumoto, director at Okasan Securities.
“Moreover, November is a historically good month for the market, and with a supporting dollar it should be able to reach fresh year-highs this week,” he told Dow Jones Newswires.
The Nikkei has surged more than 10 percent this month after the Bank of Japan ramped up its stimulus programme and the government delayed a sales tax hike planned for next year.
The yen has also fallen to multi-year lows against the dollar and euro.
In forex markets, the dollar was at 118.05 yen, from 118.25 yen in New York on Monday but still up from 117.85 yen in Tokyo on Friday.
The euro bought 147.19 yen, compared with 147.10 yen in US trade.
Toyota rose 1.31 percent to 7,182.0 yen, while Sony jumped 4.82 percent to 2,551.0 yen.
Takata soared 14.21 percent to 1,430.0 yen as the embattled auto parts company defends itself against accusations that its defective airbags led to drivers’ deaths.
Two senior US senators on Monday called for Takata to hand over 14 years of extensive records and data on the faulty airbags.-AFP